Self-standing bearing capacity of symmetric circular masonry arches at finite friction: Technical handbook of physical states

The present contribution concerns the issue of finite friction, in ruling self-standing bearing capacity and collapse modes of (symmetric circular) continuous masonry arches, with ideal inherent radial stereotomy. With primary reference, and as an enhancement, to classical “Couplet-Heyman problem”, of least-thickness form optimization, in the realm of purely-rotational collapse solutions, finite (Coulomb) friction is herein set, and thoroughly explored, in implying the possible appearance of sliding activation. The configuration of uniform (vertical) self-weight distribution is considered, herein for the true Milankovitch-like distribution accounting for the real centres of gravity of the ideal wedge-shaped chunks of the arch. The mechanical problem is analyzed, through a full analytical approach, by deriving all physical domains, and explicitly separating safe vs. collapse states of the arch. Outcomes are eventually validated by a separate dedicated Complementarity Problem/Mathematical Programming (CP/MP) numerical implementation, by fully consistent and illustrative results. Diverse key aspects are newly outlined, specifically for the representation of the characteristic solution variables as a function of friction and geometrical parameters, namely: (a) two- and three-dimensional state maps are analytically elucidated, specifically at variable arch opening; (b) underlying numerical data are thoroughly evaluated and reported in handbook tables; (c) catalogue arrays of arch geometries and collapse modes are systematically formed. The analytical-numerical achievements shall allow for a full understanding of the problem at hand, and synoptically form a technical compendium, in the Mechanics (statics) of masonry arches, and specific related role of finite friction, in providing crucial self-bearing structural capacity.